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We theoretically investigate the second harmonic generation and photon drageffect induced by an incident plane wave to a doped graphene placed on atwo-dimensional diffraction grating. The relevant nonlinear conductivity of thegraphene is obtained by a semi-classical treatment with a phenomenologicalrelaxation. The grating acts not only as a plasmon coupler but also as adispersion modulator of the graphene plasmon. As a result, the second harmonicgeneration is strongly enhanced by exciting the graphene plasmon polariton ofthe first- and/or second-harmonic frequencies. The photon drag effect is alsostrongly enhanced by the excitation of the plasmon at the first-harmonicfrequency. The direct current induced by the photon drag effect flows bothforward and backward directions to the incident light, depending on themodulated plasmon mode concerned.

Enhanced second harmonic generation and photon drag effect in a doped graphene placed on a two-dimensional diffraction grating